rotate.m

function v = rotate(v,q,varargin)
% rotate vector3d by rotation or orientation
%
% Syntax
%   v = rotate(v,20*degree) % rotation about the z-axis
%   rot = rotation.byEuler(10*degree,20*degree,30*degree)
%   v = rotate(v,rot)
%
% Description
%  Either |v| or |rot| are single elements or both have the same size. The
%  ouptut |v| will have the same size as the biger of both input arrays.
%
% Input
%  v - @vector3d
%  q - @quaternion
%
% Output
%  r - q * v
%

if isnumeric(q), q = axis2quat(zvector,q);end

if ~isa(q,'rotation')
  [a,b,c,d] = double(q);
  i = [];
else
  [a,b,c,d,i] = double(q);
end
[x,y,z] = double(v);

n = b.^2 + c.^2 + d.^2;
s = 2*(x.*b + y.*c + z.*d);

a_2 = 2*a;
a_n  = a.^2 - n;

v.x = a_2.*(c.* z - y.*d) + s.*b + a_n.*x;
v.y = a_2.*(d.* x - z.*b) + s.*c + a_n.*y;
v.z = a_2.*(b.* y - x.*c) + s.*d + a_n.*z;

if ~isempty(i) 
  if numel(i)>1
    i = logical(i);
    v.x(i) = -v.x(i);
    v.y(i) = -v.y(i);
    v.z(i) = -v.z(i);
  elseif i
    v.x = -v.x;
    v.y = -v.y;
    v.z = -v.z;
  end
end

if isa(q,'orientation')
  
  if isa(q.SS,'crystalSymmetry')
    v = Miller(v,q.SS);
    v.dispStyle = MillerConvention(v.dispStyle);
    v.dispStyle = make4Digit(v.dispStyle,q.SS);
  else % convert to vector3d 
    v = vector3d(v);
  end

end